## relaxation time

In general, the time interval required for a system exposed to some discontinuous change of environment to undergo the fraction (1 -

*e*^{-1}), or about 63%, of the total change of state that it would exhibit after an infinitely long time.For example, a thermometer initially at equilibrium in a bath at temperature

*T*_{1}will exhibit an exponential change of temperature with time after being suddenly plunged into a bath at temperature*T*_{2}, theoretically assuming the new temperature*T*_{2}only after an infinitely long time. The finite time interval required for the thermometer to undergo a change of amount (*T*_{1}-*T*_{2})(1 -*e*^{-1}) is called the thermal relaxation time of the thermometer. Occasionally, the fraction 9/10 is used in place of (1 -*e*^{-1}), so contexts must always be checked to be certain of the definition employed in a given case. The definition may also change for an underdamped device. The change of state of such a device may oscillate several times while approaching its final value.